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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 236691.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236691.q1 | 236691q2 | \([1, -1, 0, -1432338, 252581525]\) | \(684030715731/338005577\) | \(160586372103346786779\) | \([2]\) | \(6635520\) | \(2.5702\) | |
236691.q2 | 236691q1 | \([1, -1, 0, -769083, -256665664]\) | \(105890949891/1288651\) | \(612237794518254177\) | \([2]\) | \(3317760\) | \(2.2236\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236691.q have rank \(1\).
Complex multiplication
The elliptic curves in class 236691.q do not have complex multiplication.Modular form 236691.2.a.q
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.